The European Patent Application EP 1 857 217 A1 describes a method for thermally treating gas turbine blades, namely for locally thermally treating a gas turbine blade in a blade section thereof. The local heat treatment of a gas turbine blade in the blade section thereof discussed in the European Patent Application EP 1857 217 A1 provides for a blade root section, which is not to be thermally treated, of the gas turbine blade to be positioned in a fixture to prevent the blade root section, which is not to be thermally treated, from being heated during the heat treatment of the blade section by conveying a cooling medium through the fixture. To this end, the blade root section is positioned in an interior space of the fixture, the contour of the interior space being adapted to the contour of the blade root section.